| 1 | # Python test set -- math module
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| 2 | # XXXX Should not do tests around zero only
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| 3 |
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| 4 | from test.test_support import run_unittest, verbose
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| 5 | import unittest
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| 6 | import math
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| 7 | import os
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| 8 | import sys
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| 9 | import random
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| 10 | import struct
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| 11 |
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| 12 | eps = 1E-05
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| 13 | NAN = float('nan')
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| 14 | INF = float('inf')
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| 15 | NINF = float('-inf')
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| 16 |
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| 17 | # decorator for skipping tests on non-IEEE 754 platforms
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| 18 | requires_IEEE_754 = unittest.skipUnless(
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| 19 | float.__getformat__("double").startswith("IEEE"),
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| 20 | "test requires IEEE 754 doubles")
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| 21 |
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| 22 | # detect evidence of double-rounding: fsum is not always correctly
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| 23 | # rounded on machines that suffer from double rounding.
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| 24 | x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer
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| 25 | HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)
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| 26 |
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| 27 | # locate file with test values
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| 28 | if __name__ == '__main__':
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| 29 | file = sys.argv[0]
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| 30 | else:
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| 31 | file = __file__
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| 32 | test_dir = os.path.dirname(file) or os.curdir
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| 33 | math_testcases = os.path.join(test_dir, 'math_testcases.txt')
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| 34 | test_file = os.path.join(test_dir, 'cmath_testcases.txt')
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| 35 |
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| 36 | def to_ulps(x):
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| 37 | """Convert a non-NaN float x to an integer, in such a way that
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| 38 | adjacent floats are converted to adjacent integers. Then
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| 39 | abs(ulps(x) - ulps(y)) gives the difference in ulps between two
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| 40 | floats.
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| 41 |
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| 42 | The results from this function will only make sense on platforms
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| 43 | where C doubles are represented in IEEE 754 binary64 format.
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| 44 |
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| 45 | """
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| 46 | n = struct.unpack('<q', struct.pack('<d', x))[0]
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| 47 | if n < 0:
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| 48 | n = ~(n+2**63)
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| 49 | return n
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| 50 |
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| 51 | def ulps_check(expected, got, ulps=20):
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| 52 | """Given non-NaN floats `expected` and `got`,
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| 53 | check that they're equal to within the given number of ulps.
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| 54 |
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| 55 | Returns None on success and an error message on failure."""
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| 56 |
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| 57 | ulps_error = to_ulps(got) - to_ulps(expected)
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| 58 | if abs(ulps_error) <= ulps:
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| 59 | return None
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| 60 | return "error = {} ulps; permitted error = {} ulps".format(ulps_error,
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| 61 | ulps)
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| 62 |
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| 63 | def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323):
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| 64 | """Determine whether non-NaN floats a and b are equal to within a
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| 65 | (small) rounding error. The default values for rel_err and
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| 66 | abs_err are chosen to be suitable for platforms where a float is
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| 67 | represented by an IEEE 754 double. They allow an error of between
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| 68 | 9 and 19 ulps."""
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| 69 |
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| 70 | # need to special case infinities, since inf - inf gives nan
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| 71 | if math.isinf(expected) and got == expected:
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| 72 | return None
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| 73 |
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| 74 | error = got - expected
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| 75 |
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| 76 | permitted_error = max(abs_err, rel_err * abs(expected))
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| 77 | if abs(error) < permitted_error:
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| 78 | return None
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| 79 | return "error = {}; permitted error = {}".format(error,
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| 80 | permitted_error)
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| 81 |
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| 82 | def parse_mtestfile(fname):
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| 83 | """Parse a file with test values
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| 84 |
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| 85 | -- starts a comment
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| 86 | blank lines, or lines containing only a comment, are ignored
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| 87 | other lines are expected to have the form
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| 88 | id fn arg -> expected [flag]*
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| 89 |
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| 90 | """
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| 91 | with open(fname) as fp:
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| 92 | for line in fp:
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| 93 | # strip comments, and skip blank lines
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| 94 | if '--' in line:
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| 95 | line = line[:line.index('--')]
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| 96 | if not line.strip():
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| 97 | continue
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| 98 |
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| 99 | lhs, rhs = line.split('->')
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| 100 | id, fn, arg = lhs.split()
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| 101 | rhs_pieces = rhs.split()
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| 102 | exp = rhs_pieces[0]
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| 103 | flags = rhs_pieces[1:]
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| 104 |
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| 105 | yield (id, fn, float(arg), float(exp), flags)
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| 106 |
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| 107 | def parse_testfile(fname):
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| 108 | """Parse a file with test values
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| 109 |
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| 110 | Empty lines or lines starting with -- are ignored
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| 111 | yields id, fn, arg_real, arg_imag, exp_real, exp_imag
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| 112 | """
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| 113 | with open(fname) as fp:
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| 114 | for line in fp:
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| 115 | # skip comment lines and blank lines
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| 116 | if line.startswith('--') or not line.strip():
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| 117 | continue
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| 118 |
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| 119 | lhs, rhs = line.split('->')
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| 120 | id, fn, arg_real, arg_imag = lhs.split()
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| 121 | rhs_pieces = rhs.split()
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| 122 | exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
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| 123 | flags = rhs_pieces[2:]
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| 124 |
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| 125 | yield (id, fn,
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| 126 | float(arg_real), float(arg_imag),
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| 127 | float(exp_real), float(exp_imag),
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| 128 | flags
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| 129 | )
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| 130 |
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| 131 | class MathTests(unittest.TestCase):
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| 132 |
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| 133 | def ftest(self, name, value, expected):
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| 134 | if abs(value-expected) > eps:
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| 135 | # Use %r instead of %f so the error message
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| 136 | # displays full precision. Otherwise discrepancies
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| 137 | # in the last few bits will lead to very confusing
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| 138 | # error messages
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| 139 | self.fail('%s returned %r, expected %r' %
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| 140 | (name, value, expected))
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| 141 |
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| 142 | def testConstants(self):
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| 143 | self.ftest('pi', math.pi, 3.1415926)
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| 144 | self.ftest('e', math.e, 2.7182818)
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| 145 |
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| 146 | def testAcos(self):
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| 147 | self.assertRaises(TypeError, math.acos)
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| 148 | self.ftest('acos(-1)', math.acos(-1), math.pi)
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| 149 | self.ftest('acos(0)', math.acos(0), math.pi/2)
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| 150 | self.ftest('acos(1)', math.acos(1), 0)
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| 151 | self.assertRaises(ValueError, math.acos, INF)
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| 152 | self.assertRaises(ValueError, math.acos, NINF)
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| 153 | self.assertTrue(math.isnan(math.acos(NAN)))
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| 154 |
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| 155 | def testAcosh(self):
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| 156 | self.assertRaises(TypeError, math.acosh)
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| 157 | self.ftest('acosh(1)', math.acosh(1), 0)
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| 158 | self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
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| 159 | self.assertRaises(ValueError, math.acosh, 0)
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| 160 | self.assertRaises(ValueError, math.acosh, -1)
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| 161 | self.assertEqual(math.acosh(INF), INF)
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| 162 | self.assertRaises(ValueError, math.acosh, NINF)
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| 163 | self.assertTrue(math.isnan(math.acosh(NAN)))
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| 164 |
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| 165 | def testAsin(self):
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| 166 | self.assertRaises(TypeError, math.asin)
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| 167 | self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
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| 168 | self.ftest('asin(0)', math.asin(0), 0)
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| 169 | self.ftest('asin(1)', math.asin(1), math.pi/2)
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| 170 | self.assertRaises(ValueError, math.asin, INF)
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| 171 | self.assertRaises(ValueError, math.asin, NINF)
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| 172 | self.assertTrue(math.isnan(math.asin(NAN)))
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| 173 |
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| 174 | def testAsinh(self):
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| 175 | self.assertRaises(TypeError, math.asinh)
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| 176 | self.ftest('asinh(0)', math.asinh(0), 0)
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| 177 | self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
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| 178 | self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
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| 179 | self.assertEqual(math.asinh(INF), INF)
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| 180 | self.assertEqual(math.asinh(NINF), NINF)
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| 181 | self.assertTrue(math.isnan(math.asinh(NAN)))
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| 182 |
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| 183 | def testAtan(self):
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| 184 | self.assertRaises(TypeError, math.atan)
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| 185 | self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
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| 186 | self.ftest('atan(0)', math.atan(0), 0)
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| 187 | self.ftest('atan(1)', math.atan(1), math.pi/4)
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| 188 | self.ftest('atan(inf)', math.atan(INF), math.pi/2)
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| 189 | self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
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| 190 | self.assertTrue(math.isnan(math.atan(NAN)))
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| 191 |
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| 192 | def testAtanh(self):
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| 193 | self.assertRaises(TypeError, math.atan)
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| 194 | self.ftest('atanh(0)', math.atanh(0), 0)
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| 195 | self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
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| 196 | self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
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| 197 | self.assertRaises(ValueError, math.atanh, 1)
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| 198 | self.assertRaises(ValueError, math.atanh, -1)
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| 199 | self.assertRaises(ValueError, math.atanh, INF)
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| 200 | self.assertRaises(ValueError, math.atanh, NINF)
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| 201 | self.assertTrue(math.isnan(math.atanh(NAN)))
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| 202 |
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| 203 | def testAtan2(self):
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| 204 | self.assertRaises(TypeError, math.atan2)
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| 205 | self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
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| 206 | self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
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| 207 | self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
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| 208 | self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
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| 209 | self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
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| 210 |
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| 211 | # math.atan2(0, x)
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| 212 | self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
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| 213 | self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
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| 214 | self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
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| 215 | self.assertEqual(math.atan2(0., 0.), 0.)
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| 216 | self.assertEqual(math.atan2(0., 2.3), 0.)
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| 217 | self.assertEqual(math.atan2(0., INF), 0.)
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| 218 | self.assertTrue(math.isnan(math.atan2(0., NAN)))
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| 219 | # math.atan2(-0, x)
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| 220 | self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
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| 221 | self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
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| 222 | self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
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| 223 | self.assertEqual(math.atan2(-0., 0.), -0.)
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| 224 | self.assertEqual(math.atan2(-0., 2.3), -0.)
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| 225 | self.assertEqual(math.atan2(-0., INF), -0.)
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| 226 | self.assertTrue(math.isnan(math.atan2(-0., NAN)))
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| 227 | # math.atan2(INF, x)
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| 228 | self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
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| 229 | self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
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| 230 | self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
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| 231 | self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
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| 232 | self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
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| 233 | self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
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| 234 | self.assertTrue(math.isnan(math.atan2(INF, NAN)))
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| 235 | # math.atan2(NINF, x)
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| 236 | self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
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| 237 | self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
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| 238 | self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
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| 239 | self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
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| 240 | self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
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| 241 | self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
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| 242 | self.assertTrue(math.isnan(math.atan2(NINF, NAN)))
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| 243 | # math.atan2(+finite, x)
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| 244 | self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
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| 245 | self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
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| 246 | self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
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| 247 | self.assertEqual(math.atan2(2.3, INF), 0.)
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| 248 | self.assertTrue(math.isnan(math.atan2(2.3, NAN)))
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| 249 | # math.atan2(-finite, x)
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| 250 | self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
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| 251 | self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
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| 252 | self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
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| 253 | self.assertEqual(math.atan2(-2.3, INF), -0.)
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| 254 | self.assertTrue(math.isnan(math.atan2(-2.3, NAN)))
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| 255 | # math.atan2(NAN, x)
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| 256 | self.assertTrue(math.isnan(math.atan2(NAN, NINF)))
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| 257 | self.assertTrue(math.isnan(math.atan2(NAN, -2.3)))
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| 258 | self.assertTrue(math.isnan(math.atan2(NAN, -0.)))
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| 259 | self.assertTrue(math.isnan(math.atan2(NAN, 0.)))
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| 260 | self.assertTrue(math.isnan(math.atan2(NAN, 2.3)))
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| 261 | self.assertTrue(math.isnan(math.atan2(NAN, INF)))
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| 262 | self.assertTrue(math.isnan(math.atan2(NAN, NAN)))
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| 263 |
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| 264 | def testCeil(self):
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| 265 | self.assertRaises(TypeError, math.ceil)
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| 266 | # These types will be int in py3k.
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| 267 | self.assertEqual(float, type(math.ceil(1)))
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| 268 | self.assertEqual(float, type(math.ceil(1L)))
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| 269 | self.assertEqual(float, type(math.ceil(1.0)))
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| 270 | self.ftest('ceil(0.5)', math.ceil(0.5), 1)
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| 271 | self.ftest('ceil(1.0)', math.ceil(1.0), 1)
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| 272 | self.ftest('ceil(1.5)', math.ceil(1.5), 2)
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| 273 | self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
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| 274 | self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
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| 275 | self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
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| 276 | self.assertEqual(math.ceil(INF), INF)
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| 277 | self.assertEqual(math.ceil(NINF), NINF)
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| 278 | self.assertTrue(math.isnan(math.ceil(NAN)))
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| 279 |
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| 280 | class TestCeil(object):
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| 281 | def __float__(self):
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| 282 | return 41.3
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| 283 | class TestNoCeil(object):
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| 284 | pass
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| 285 | self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
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| 286 | self.assertRaises(TypeError, math.ceil, TestNoCeil())
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| 287 |
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| 288 | t = TestNoCeil()
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| 289 | t.__ceil__ = lambda *args: args
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| 290 | self.assertRaises(TypeError, math.ceil, t)
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| 291 | self.assertRaises(TypeError, math.ceil, t, 0)
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| 292 |
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| 293 | @requires_IEEE_754
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| 294 | def testCopysign(self):
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| 295 | self.assertEqual(math.copysign(1, 42), 1.0)
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| 296 | self.assertEqual(math.copysign(0., 42), 0.0)
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| 297 | self.assertEqual(math.copysign(1., -42), -1.0)
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| 298 | self.assertEqual(math.copysign(3, 0.), 3.0)
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| 299 | self.assertEqual(math.copysign(4., -0.), -4.0)
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| 300 |
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| 301 | self.assertRaises(TypeError, math.copysign)
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| 302 | # copysign should let us distinguish signs of zeros
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| 303 | self.assertEqual(math.copysign(1., 0.), 1.)
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| 304 | self.assertEqual(math.copysign(1., -0.), -1.)
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| 305 | self.assertEqual(math.copysign(INF, 0.), INF)
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| 306 | self.assertEqual(math.copysign(INF, -0.), NINF)
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| 307 | self.assertEqual(math.copysign(NINF, 0.), INF)
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| 308 | self.assertEqual(math.copysign(NINF, -0.), NINF)
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| 309 | # and of infinities
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| 310 | self.assertEqual(math.copysign(1., INF), 1.)
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| 311 | self.assertEqual(math.copysign(1., NINF), -1.)
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| 312 | self.assertEqual(math.copysign(INF, INF), INF)
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| 313 | self.assertEqual(math.copysign(INF, NINF), NINF)
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| 314 | self.assertEqual(math.copysign(NINF, INF), INF)
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| 315 | self.assertEqual(math.copysign(NINF, NINF), NINF)
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| 316 | self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
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| 317 | self.assertTrue(math.isnan(math.copysign(NAN, INF)))
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| 318 | self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
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| 319 | self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
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| 320 | # copysign(INF, NAN) may be INF or it may be NINF, since
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| 321 | # we don't know whether the sign bit of NAN is set on any
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| 322 | # given platform.
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| 323 | self.assertTrue(math.isinf(math.copysign(INF, NAN)))
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| 324 | # similarly, copysign(2., NAN) could be 2. or -2.
|
|---|
| 325 | self.assertEqual(abs(math.copysign(2., NAN)), 2.)
|
|---|
| 326 |
|
|---|
| 327 | def testCos(self):
|
|---|
| 328 | self.assertRaises(TypeError, math.cos)
|
|---|
| 329 | self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
|
|---|
| 330 | self.ftest('cos(0)', math.cos(0), 1)
|
|---|
| 331 | self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
|
|---|
| 332 | self.ftest('cos(pi)', math.cos(math.pi), -1)
|
|---|
| 333 | try:
|
|---|
| 334 | self.assertTrue(math.isnan(math.cos(INF)))
|
|---|
| 335 | self.assertTrue(math.isnan(math.cos(NINF)))
|
|---|
| 336 | except ValueError:
|
|---|
| 337 | self.assertRaises(ValueError, math.cos, INF)
|
|---|
| 338 | self.assertRaises(ValueError, math.cos, NINF)
|
|---|
| 339 | self.assertTrue(math.isnan(math.cos(NAN)))
|
|---|
| 340 |
|
|---|
| 341 | def testCosh(self):
|
|---|
| 342 | self.assertRaises(TypeError, math.cosh)
|
|---|
| 343 | self.ftest('cosh(0)', math.cosh(0), 1)
|
|---|
| 344 | self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
|
|---|
| 345 | self.assertEqual(math.cosh(INF), INF)
|
|---|
| 346 | self.assertEqual(math.cosh(NINF), INF)
|
|---|
| 347 | self.assertTrue(math.isnan(math.cosh(NAN)))
|
|---|
| 348 |
|
|---|
| 349 | def testDegrees(self):
|
|---|
| 350 | self.assertRaises(TypeError, math.degrees)
|
|---|
| 351 | self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
|
|---|
| 352 | self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
|
|---|
| 353 | self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
|
|---|
| 354 |
|
|---|
| 355 | def testExp(self):
|
|---|
| 356 | self.assertRaises(TypeError, math.exp)
|
|---|
| 357 | self.ftest('exp(-1)', math.exp(-1), 1/math.e)
|
|---|
| 358 | self.ftest('exp(0)', math.exp(0), 1)
|
|---|
| 359 | self.ftest('exp(1)', math.exp(1), math.e)
|
|---|
| 360 | self.assertEqual(math.exp(INF), INF)
|
|---|
| 361 | self.assertEqual(math.exp(NINF), 0.)
|
|---|
| 362 | self.assertTrue(math.isnan(math.exp(NAN)))
|
|---|
| 363 |
|
|---|
| 364 | def testFabs(self):
|
|---|
| 365 | self.assertRaises(TypeError, math.fabs)
|
|---|
| 366 | self.ftest('fabs(-1)', math.fabs(-1), 1)
|
|---|
| 367 | self.ftest('fabs(0)', math.fabs(0), 0)
|
|---|
| 368 | self.ftest('fabs(1)', math.fabs(1), 1)
|
|---|
| 369 |
|
|---|
| 370 | def testFactorial(self):
|
|---|
| 371 | def fact(n):
|
|---|
| 372 | result = 1
|
|---|
| 373 | for i in range(1, int(n)+1):
|
|---|
| 374 | result *= i
|
|---|
| 375 | return result
|
|---|
| 376 | values = range(10) + [50, 100, 500]
|
|---|
| 377 | random.shuffle(values)
|
|---|
| 378 | for x in values:
|
|---|
| 379 | for cast in (int, long, float):
|
|---|
| 380 | self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x)))
|
|---|
| 381 | self.assertRaises(ValueError, math.factorial, -1)
|
|---|
| 382 | self.assertRaises(ValueError, math.factorial, math.pi)
|
|---|
| 383 |
|
|---|
| 384 | def testFloor(self):
|
|---|
| 385 | self.assertRaises(TypeError, math.floor)
|
|---|
| 386 | # These types will be int in py3k.
|
|---|
| 387 | self.assertEqual(float, type(math.floor(1)))
|
|---|
| 388 | self.assertEqual(float, type(math.floor(1L)))
|
|---|
| 389 | self.assertEqual(float, type(math.floor(1.0)))
|
|---|
| 390 | self.ftest('floor(0.5)', math.floor(0.5), 0)
|
|---|
| 391 | self.ftest('floor(1.0)', math.floor(1.0), 1)
|
|---|
| 392 | self.ftest('floor(1.5)', math.floor(1.5), 1)
|
|---|
| 393 | self.ftest('floor(-0.5)', math.floor(-0.5), -1)
|
|---|
| 394 | self.ftest('floor(-1.0)', math.floor(-1.0), -1)
|
|---|
| 395 | self.ftest('floor(-1.5)', math.floor(-1.5), -2)
|
|---|
| 396 | # pow() relies on floor() to check for integers
|
|---|
| 397 | # This fails on some platforms - so check it here
|
|---|
| 398 | self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
|
|---|
| 399 | self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
|
|---|
| 400 | self.assertEqual(math.ceil(INF), INF)
|
|---|
| 401 | self.assertEqual(math.ceil(NINF), NINF)
|
|---|
| 402 | self.assertTrue(math.isnan(math.floor(NAN)))
|
|---|
| 403 |
|
|---|
| 404 | class TestFloor(object):
|
|---|
| 405 | def __float__(self):
|
|---|
| 406 | return 42.3
|
|---|
| 407 | class TestNoFloor(object):
|
|---|
| 408 | pass
|
|---|
| 409 | self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
|
|---|
| 410 | self.assertRaises(TypeError, math.floor, TestNoFloor())
|
|---|
| 411 |
|
|---|
| 412 | t = TestNoFloor()
|
|---|
| 413 | t.__floor__ = lambda *args: args
|
|---|
| 414 | self.assertRaises(TypeError, math.floor, t)
|
|---|
| 415 | self.assertRaises(TypeError, math.floor, t, 0)
|
|---|
| 416 |
|
|---|
| 417 | def testFmod(self):
|
|---|
| 418 | self.assertRaises(TypeError, math.fmod)
|
|---|
| 419 | self.ftest('fmod(10,1)', math.fmod(10,1), 0)
|
|---|
| 420 | self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)
|
|---|
| 421 | self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)
|
|---|
| 422 | self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
|
|---|
| 423 | self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
|
|---|
| 424 | self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)
|
|---|
| 425 | self.assertTrue(math.isnan(math.fmod(NAN, 1.)))
|
|---|
| 426 | self.assertTrue(math.isnan(math.fmod(1., NAN)))
|
|---|
| 427 | self.assertTrue(math.isnan(math.fmod(NAN, NAN)))
|
|---|
| 428 | self.assertRaises(ValueError, math.fmod, 1., 0.)
|
|---|
| 429 | self.assertRaises(ValueError, math.fmod, INF, 1.)
|
|---|
| 430 | self.assertRaises(ValueError, math.fmod, NINF, 1.)
|
|---|
| 431 | self.assertRaises(ValueError, math.fmod, INF, 0.)
|
|---|
| 432 | self.assertEqual(math.fmod(3.0, INF), 3.0)
|
|---|
| 433 | self.assertEqual(math.fmod(-3.0, INF), -3.0)
|
|---|
| 434 | self.assertEqual(math.fmod(3.0, NINF), 3.0)
|
|---|
| 435 | self.assertEqual(math.fmod(-3.0, NINF), -3.0)
|
|---|
| 436 | self.assertEqual(math.fmod(0.0, 3.0), 0.0)
|
|---|
| 437 | self.assertEqual(math.fmod(0.0, NINF), 0.0)
|
|---|
| 438 |
|
|---|
| 439 | def testFrexp(self):
|
|---|
| 440 | self.assertRaises(TypeError, math.frexp)
|
|---|
| 441 |
|
|---|
| 442 | def testfrexp(name, result, expected):
|
|---|
| 443 | (mant, exp), (emant, eexp) = result, expected
|
|---|
| 444 | if abs(mant-emant) > eps or exp != eexp:
|
|---|
| 445 | self.fail('%s returned %r, expected %r'%\
|
|---|
| 446 | (name, (mant, exp), (emant,eexp)))
|
|---|
| 447 |
|
|---|
| 448 | testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
|
|---|
| 449 | testfrexp('frexp(0)', math.frexp(0), (0, 0))
|
|---|
| 450 | testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
|
|---|
| 451 | testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
|
|---|
| 452 |
|
|---|
| 453 | self.assertEqual(math.frexp(INF)[0], INF)
|
|---|
| 454 | self.assertEqual(math.frexp(NINF)[0], NINF)
|
|---|
| 455 | self.assertTrue(math.isnan(math.frexp(NAN)[0]))
|
|---|
| 456 |
|
|---|
| 457 | @requires_IEEE_754
|
|---|
| 458 | @unittest.skipIf(HAVE_DOUBLE_ROUNDING,
|
|---|
| 459 | "fsum is not exact on machines with double rounding")
|
|---|
| 460 | def testFsum(self):
|
|---|
| 461 | # math.fsum relies on exact rounding for correct operation.
|
|---|
| 462 | # There's a known problem with IA32 floating-point that causes
|
|---|
| 463 | # inexact rounding in some situations, and will cause the
|
|---|
| 464 | # math.fsum tests below to fail; see issue #2937. On non IEEE
|
|---|
| 465 | # 754 platforms, and on IEEE 754 platforms that exhibit the
|
|---|
| 466 | # problem described in issue #2937, we simply skip the whole
|
|---|
| 467 | # test.
|
|---|
| 468 |
|
|---|
| 469 | # Python version of math.fsum, for comparison. Uses a
|
|---|
| 470 | # different algorithm based on frexp, ldexp and integer
|
|---|
| 471 | # arithmetic.
|
|---|
| 472 | from sys import float_info
|
|---|
| 473 | mant_dig = float_info.mant_dig
|
|---|
| 474 | etiny = float_info.min_exp - mant_dig
|
|---|
| 475 |
|
|---|
| 476 | def msum(iterable):
|
|---|
| 477 | """Full precision summation. Compute sum(iterable) without any
|
|---|
| 478 | intermediate accumulation of error. Based on the 'lsum' function
|
|---|
| 479 | at http://code.activestate.com/recipes/393090/
|
|---|
| 480 |
|
|---|
| 481 | """
|
|---|
| 482 | tmant, texp = 0, 0
|
|---|
| 483 | for x in iterable:
|
|---|
| 484 | mant, exp = math.frexp(x)
|
|---|
| 485 | mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
|
|---|
| 486 | if texp > exp:
|
|---|
| 487 | tmant <<= texp-exp
|
|---|
| 488 | texp = exp
|
|---|
| 489 | else:
|
|---|
| 490 | mant <<= exp-texp
|
|---|
| 491 | tmant += mant
|
|---|
| 492 | # Round tmant * 2**texp to a float. The original recipe
|
|---|
| 493 | # used float(str(tmant)) * 2.0**texp for this, but that's
|
|---|
| 494 | # a little unsafe because str -> float conversion can't be
|
|---|
| 495 | # relied upon to do correct rounding on all platforms.
|
|---|
| 496 | tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
|
|---|
| 497 | if tail > 0:
|
|---|
| 498 | h = 1 << (tail-1)
|
|---|
| 499 | tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
|
|---|
| 500 | texp += tail
|
|---|
| 501 | return math.ldexp(tmant, texp)
|
|---|
| 502 |
|
|---|
| 503 | test_values = [
|
|---|
| 504 | ([], 0.0),
|
|---|
| 505 | ([0.0], 0.0),
|
|---|
| 506 | ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
|
|---|
| 507 | ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
|
|---|
| 508 | ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
|
|---|
| 509 | ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
|
|---|
| 510 | ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
|
|---|
| 511 | ([1./n for n in range(1, 1001)],
|
|---|
| 512 | float.fromhex('0x1.df11f45f4e61ap+2')),
|
|---|
| 513 | ([(-1.)**n/n for n in range(1, 1001)],
|
|---|
| 514 | float.fromhex('-0x1.62a2af1bd3624p-1')),
|
|---|
| 515 | ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),
|
|---|
| 516 | ([1e16, 1., 1e-16], 10000000000000002.0),
|
|---|
| 517 | ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),
|
|---|
| 518 | # exercise code for resizing partials array
|
|---|
| 519 | ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
|
|---|
| 520 | [-2.**1022],
|
|---|
| 521 | float.fromhex('0x1.5555555555555p+970')),
|
|---|
| 522 | ]
|
|---|
| 523 |
|
|---|
| 524 | for i, (vals, expected) in enumerate(test_values):
|
|---|
| 525 | try:
|
|---|
| 526 | actual = math.fsum(vals)
|
|---|
| 527 | except OverflowError:
|
|---|
| 528 | self.fail("test %d failed: got OverflowError, expected %r "
|
|---|
| 529 | "for math.fsum(%.100r)" % (i, expected, vals))
|
|---|
| 530 | except ValueError:
|
|---|
| 531 | self.fail("test %d failed: got ValueError, expected %r "
|
|---|
| 532 | "for math.fsum(%.100r)" % (i, expected, vals))
|
|---|
| 533 | self.assertEqual(actual, expected)
|
|---|
| 534 |
|
|---|
| 535 | from random import random, gauss, shuffle
|
|---|
| 536 | for j in xrange(1000):
|
|---|
| 537 | vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
|
|---|
| 538 | s = 0
|
|---|
| 539 | for i in xrange(200):
|
|---|
| 540 | v = gauss(0, random()) ** 7 - s
|
|---|
| 541 | s += v
|
|---|
| 542 | vals.append(v)
|
|---|
| 543 | shuffle(vals)
|
|---|
| 544 |
|
|---|
| 545 | s = msum(vals)
|
|---|
| 546 | self.assertEqual(msum(vals), math.fsum(vals))
|
|---|
| 547 |
|
|---|
| 548 | def testHypot(self):
|
|---|
| 549 | self.assertRaises(TypeError, math.hypot)
|
|---|
| 550 | self.ftest('hypot(0,0)', math.hypot(0,0), 0)
|
|---|
| 551 | self.ftest('hypot(3,4)', math.hypot(3,4), 5)
|
|---|
| 552 | self.assertEqual(math.hypot(NAN, INF), INF)
|
|---|
| 553 | self.assertEqual(math.hypot(INF, NAN), INF)
|
|---|
| 554 | self.assertEqual(math.hypot(NAN, NINF), INF)
|
|---|
| 555 | self.assertEqual(math.hypot(NINF, NAN), INF)
|
|---|
| 556 | self.assertTrue(math.isnan(math.hypot(1.0, NAN)))
|
|---|
| 557 | self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))
|
|---|
| 558 |
|
|---|
| 559 | def testLdexp(self):
|
|---|
| 560 | self.assertRaises(TypeError, math.ldexp)
|
|---|
| 561 | self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
|
|---|
| 562 | self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
|
|---|
| 563 | self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
|
|---|
| 564 | self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
|
|---|
| 565 | self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
|
|---|
| 566 | self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
|
|---|
| 567 | self.assertEqual(math.ldexp(1., -1000000), 0.)
|
|---|
| 568 | self.assertEqual(math.ldexp(-1., -1000000), -0.)
|
|---|
| 569 | self.assertEqual(math.ldexp(INF, 30), INF)
|
|---|
| 570 | self.assertEqual(math.ldexp(NINF, -213), NINF)
|
|---|
| 571 | self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
|
|---|
| 572 |
|
|---|
| 573 | # large second argument
|
|---|
| 574 | for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
|
|---|
| 575 | self.assertEqual(math.ldexp(INF, -n), INF)
|
|---|
| 576 | self.assertEqual(math.ldexp(NINF, -n), NINF)
|
|---|
| 577 | self.assertEqual(math.ldexp(1., -n), 0.)
|
|---|
| 578 | self.assertEqual(math.ldexp(-1., -n), -0.)
|
|---|
| 579 | self.assertEqual(math.ldexp(0., -n), 0.)
|
|---|
| 580 | self.assertEqual(math.ldexp(-0., -n), -0.)
|
|---|
| 581 | self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
|
|---|
| 582 |
|
|---|
| 583 | self.assertRaises(OverflowError, math.ldexp, 1., n)
|
|---|
| 584 | self.assertRaises(OverflowError, math.ldexp, -1., n)
|
|---|
| 585 | self.assertEqual(math.ldexp(0., n), 0.)
|
|---|
| 586 | self.assertEqual(math.ldexp(-0., n), -0.)
|
|---|
| 587 | self.assertEqual(math.ldexp(INF, n), INF)
|
|---|
| 588 | self.assertEqual(math.ldexp(NINF, n), NINF)
|
|---|
| 589 | self.assertTrue(math.isnan(math.ldexp(NAN, n)))
|
|---|
| 590 |
|
|---|
| 591 | def testLog(self):
|
|---|
| 592 | self.assertRaises(TypeError, math.log)
|
|---|
| 593 | self.ftest('log(1/e)', math.log(1/math.e), -1)
|
|---|
| 594 | self.ftest('log(1)', math.log(1), 0)
|
|---|
| 595 | self.ftest('log(e)', math.log(math.e), 1)
|
|---|
| 596 | self.ftest('log(32,2)', math.log(32,2), 5)
|
|---|
| 597 | self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
|
|---|
| 598 | self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
|
|---|
| 599 | self.assertEqual(math.log(INF), INF)
|
|---|
| 600 | self.assertRaises(ValueError, math.log, NINF)
|
|---|
| 601 | self.assertTrue(math.isnan(math.log(NAN)))
|
|---|
| 602 | # Log values should match for int and long (issue #18739).
|
|---|
| 603 | for n in range(1, 1000):
|
|---|
| 604 | self.assertEqual(math.log(n), math.log(long(n)))
|
|---|
| 605 |
|
|---|
| 606 | def testLog1p(self):
|
|---|
| 607 | self.assertRaises(TypeError, math.log1p)
|
|---|
| 608 | self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)
|
|---|
| 609 | self.ftest('log1p(0)', math.log1p(0), 0)
|
|---|
| 610 | self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)
|
|---|
| 611 | self.ftest('log1p(1)', math.log1p(1), math.log(2))
|
|---|
| 612 | self.assertEqual(math.log1p(INF), INF)
|
|---|
| 613 | self.assertRaises(ValueError, math.log1p, NINF)
|
|---|
| 614 | self.assertTrue(math.isnan(math.log1p(NAN)))
|
|---|
| 615 | n= 2**90
|
|---|
| 616 | self.assertAlmostEqual(math.log1p(n), 62.383246250395075)
|
|---|
| 617 | self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))
|
|---|
| 618 |
|
|---|
| 619 | def testLog10(self):
|
|---|
| 620 | self.assertRaises(TypeError, math.log10)
|
|---|
| 621 | self.ftest('log10(0.1)', math.log10(0.1), -1)
|
|---|
| 622 | self.ftest('log10(1)', math.log10(1), 0)
|
|---|
| 623 | self.ftest('log10(10)', math.log10(10), 1)
|
|---|
| 624 | self.assertEqual(math.log(INF), INF)
|
|---|
| 625 | self.assertRaises(ValueError, math.log10, NINF)
|
|---|
| 626 | self.assertTrue(math.isnan(math.log10(NAN)))
|
|---|
| 627 | # Log values should match for int and long (issue #18739).
|
|---|
| 628 | for n in range(1, 1000):
|
|---|
| 629 | self.assertEqual(math.log10(n), math.log10(long(n)))
|
|---|
| 630 |
|
|---|
| 631 | def testModf(self):
|
|---|
| 632 | self.assertRaises(TypeError, math.modf)
|
|---|
| 633 |
|
|---|
| 634 | def testmodf(name, result, expected):
|
|---|
| 635 | (v1, v2), (e1, e2) = result, expected
|
|---|
| 636 | if abs(v1-e1) > eps or abs(v2-e2):
|
|---|
| 637 | self.fail('%s returned %r, expected %r'%\
|
|---|
| 638 | (name, (v1,v2), (e1,e2)))
|
|---|
| 639 |
|
|---|
| 640 | testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
|
|---|
| 641 | testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
|
|---|
| 642 |
|
|---|
| 643 | self.assertEqual(math.modf(INF), (0.0, INF))
|
|---|
| 644 | self.assertEqual(math.modf(NINF), (-0.0, NINF))
|
|---|
| 645 |
|
|---|
| 646 | modf_nan = math.modf(NAN)
|
|---|
| 647 | self.assertTrue(math.isnan(modf_nan[0]))
|
|---|
| 648 | self.assertTrue(math.isnan(modf_nan[1]))
|
|---|
| 649 |
|
|---|
| 650 | def testPow(self):
|
|---|
| 651 | self.assertRaises(TypeError, math.pow)
|
|---|
| 652 | self.ftest('pow(0,1)', math.pow(0,1), 0)
|
|---|
| 653 | self.ftest('pow(1,0)', math.pow(1,0), 1)
|
|---|
| 654 | self.ftest('pow(2,1)', math.pow(2,1), 2)
|
|---|
| 655 | self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
|
|---|
| 656 | self.assertEqual(math.pow(INF, 1), INF)
|
|---|
| 657 | self.assertEqual(math.pow(NINF, 1), NINF)
|
|---|
| 658 | self.assertEqual((math.pow(1, INF)), 1.)
|
|---|
| 659 | self.assertEqual((math.pow(1, NINF)), 1.)
|
|---|
| 660 | self.assertTrue(math.isnan(math.pow(NAN, 1)))
|
|---|
| 661 | self.assertTrue(math.isnan(math.pow(2, NAN)))
|
|---|
| 662 | self.assertTrue(math.isnan(math.pow(0, NAN)))
|
|---|
| 663 | self.assertEqual(math.pow(1, NAN), 1)
|
|---|
| 664 |
|
|---|
| 665 | # pow(0., x)
|
|---|
| 666 | self.assertEqual(math.pow(0., INF), 0.)
|
|---|
| 667 | self.assertEqual(math.pow(0., 3.), 0.)
|
|---|
| 668 | self.assertEqual(math.pow(0., 2.3), 0.)
|
|---|
| 669 | self.assertEqual(math.pow(0., 2.), 0.)
|
|---|
| 670 | self.assertEqual(math.pow(0., 0.), 1.)
|
|---|
| 671 | self.assertEqual(math.pow(0., -0.), 1.)
|
|---|
| 672 | self.assertRaises(ValueError, math.pow, 0., -2.)
|
|---|
| 673 | self.assertRaises(ValueError, math.pow, 0., -2.3)
|
|---|
| 674 | self.assertRaises(ValueError, math.pow, 0., -3.)
|
|---|
| 675 | self.assertRaises(ValueError, math.pow, 0., NINF)
|
|---|
| 676 | self.assertTrue(math.isnan(math.pow(0., NAN)))
|
|---|
| 677 |
|
|---|
| 678 | # pow(INF, x)
|
|---|
| 679 | self.assertEqual(math.pow(INF, INF), INF)
|
|---|
| 680 | self.assertEqual(math.pow(INF, 3.), INF)
|
|---|
| 681 | self.assertEqual(math.pow(INF, 2.3), INF)
|
|---|
| 682 | self.assertEqual(math.pow(INF, 2.), INF)
|
|---|
| 683 | self.assertEqual(math.pow(INF, 0.), 1.)
|
|---|
| 684 | self.assertEqual(math.pow(INF, -0.), 1.)
|
|---|
| 685 | self.assertEqual(math.pow(INF, -2.), 0.)
|
|---|
| 686 | self.assertEqual(math.pow(INF, -2.3), 0.)
|
|---|
| 687 | self.assertEqual(math.pow(INF, -3.), 0.)
|
|---|
| 688 | self.assertEqual(math.pow(INF, NINF), 0.)
|
|---|
| 689 | self.assertTrue(math.isnan(math.pow(INF, NAN)))
|
|---|
| 690 |
|
|---|
| 691 | # pow(-0., x)
|
|---|
| 692 | self.assertEqual(math.pow(-0., INF), 0.)
|
|---|
| 693 | self.assertEqual(math.pow(-0., 3.), -0.)
|
|---|
| 694 | self.assertEqual(math.pow(-0., 2.3), 0.)
|
|---|
| 695 | self.assertEqual(math.pow(-0., 2.), 0.)
|
|---|
| 696 | self.assertEqual(math.pow(-0., 0.), 1.)
|
|---|
| 697 | self.assertEqual(math.pow(-0., -0.), 1.)
|
|---|
| 698 | self.assertRaises(ValueError, math.pow, -0., -2.)
|
|---|
| 699 | self.assertRaises(ValueError, math.pow, -0., -2.3)
|
|---|
| 700 | self.assertRaises(ValueError, math.pow, -0., -3.)
|
|---|
| 701 | self.assertRaises(ValueError, math.pow, -0., NINF)
|
|---|
| 702 | self.assertTrue(math.isnan(math.pow(-0., NAN)))
|
|---|
| 703 |
|
|---|
| 704 | # pow(NINF, x)
|
|---|
| 705 | self.assertEqual(math.pow(NINF, INF), INF)
|
|---|
| 706 | self.assertEqual(math.pow(NINF, 3.), NINF)
|
|---|
| 707 | self.assertEqual(math.pow(NINF, 2.3), INF)
|
|---|
| 708 | self.assertEqual(math.pow(NINF, 2.), INF)
|
|---|
| 709 | self.assertEqual(math.pow(NINF, 0.), 1.)
|
|---|
| 710 | self.assertEqual(math.pow(NINF, -0.), 1.)
|
|---|
| 711 | self.assertEqual(math.pow(NINF, -2.), 0.)
|
|---|
| 712 | self.assertEqual(math.pow(NINF, -2.3), 0.)
|
|---|
| 713 | self.assertEqual(math.pow(NINF, -3.), -0.)
|
|---|
| 714 | self.assertEqual(math.pow(NINF, NINF), 0.)
|
|---|
| 715 | self.assertTrue(math.isnan(math.pow(NINF, NAN)))
|
|---|
| 716 |
|
|---|
| 717 | # pow(-1, x)
|
|---|
| 718 | self.assertEqual(math.pow(-1., INF), 1.)
|
|---|
| 719 | self.assertEqual(math.pow(-1., 3.), -1.)
|
|---|
| 720 | self.assertRaises(ValueError, math.pow, -1., 2.3)
|
|---|
| 721 | self.assertEqual(math.pow(-1., 2.), 1.)
|
|---|
| 722 | self.assertEqual(math.pow(-1., 0.), 1.)
|
|---|
| 723 | self.assertEqual(math.pow(-1., -0.), 1.)
|
|---|
| 724 | self.assertEqual(math.pow(-1., -2.), 1.)
|
|---|
| 725 | self.assertRaises(ValueError, math.pow, -1., -2.3)
|
|---|
| 726 | self.assertEqual(math.pow(-1., -3.), -1.)
|
|---|
| 727 | self.assertEqual(math.pow(-1., NINF), 1.)
|
|---|
| 728 | self.assertTrue(math.isnan(math.pow(-1., NAN)))
|
|---|
| 729 |
|
|---|
| 730 | # pow(1, x)
|
|---|
| 731 | self.assertEqual(math.pow(1., INF), 1.)
|
|---|
| 732 | self.assertEqual(math.pow(1., 3.), 1.)
|
|---|
| 733 | self.assertEqual(math.pow(1., 2.3), 1.)
|
|---|
| 734 | self.assertEqual(math.pow(1., 2.), 1.)
|
|---|
| 735 | self.assertEqual(math.pow(1., 0.), 1.)
|
|---|
| 736 | self.assertEqual(math.pow(1., -0.), 1.)
|
|---|
| 737 | self.assertEqual(math.pow(1., -2.), 1.)
|
|---|
| 738 | self.assertEqual(math.pow(1., -2.3), 1.)
|
|---|
| 739 | self.assertEqual(math.pow(1., -3.), 1.)
|
|---|
| 740 | self.assertEqual(math.pow(1., NINF), 1.)
|
|---|
| 741 | self.assertEqual(math.pow(1., NAN), 1.)
|
|---|
| 742 |
|
|---|
| 743 | # pow(x, 0) should be 1 for any x
|
|---|
| 744 | self.assertEqual(math.pow(2.3, 0.), 1.)
|
|---|
| 745 | self.assertEqual(math.pow(-2.3, 0.), 1.)
|
|---|
| 746 | self.assertEqual(math.pow(NAN, 0.), 1.)
|
|---|
| 747 | self.assertEqual(math.pow(2.3, -0.), 1.)
|
|---|
| 748 | self.assertEqual(math.pow(-2.3, -0.), 1.)
|
|---|
| 749 | self.assertEqual(math.pow(NAN, -0.), 1.)
|
|---|
| 750 |
|
|---|
| 751 | # pow(x, y) is invalid if x is negative and y is not integral
|
|---|
| 752 | self.assertRaises(ValueError, math.pow, -1., 2.3)
|
|---|
| 753 | self.assertRaises(ValueError, math.pow, -15., -3.1)
|
|---|
| 754 |
|
|---|
| 755 | # pow(x, NINF)
|
|---|
| 756 | self.assertEqual(math.pow(1.9, NINF), 0.)
|
|---|
| 757 | self.assertEqual(math.pow(1.1, NINF), 0.)
|
|---|
| 758 | self.assertEqual(math.pow(0.9, NINF), INF)
|
|---|
| 759 | self.assertEqual(math.pow(0.1, NINF), INF)
|
|---|
| 760 | self.assertEqual(math.pow(-0.1, NINF), INF)
|
|---|
| 761 | self.assertEqual(math.pow(-0.9, NINF), INF)
|
|---|
| 762 | self.assertEqual(math.pow(-1.1, NINF), 0.)
|
|---|
| 763 | self.assertEqual(math.pow(-1.9, NINF), 0.)
|
|---|
| 764 |
|
|---|
| 765 | # pow(x, INF)
|
|---|
| 766 | self.assertEqual(math.pow(1.9, INF), INF)
|
|---|
| 767 | self.assertEqual(math.pow(1.1, INF), INF)
|
|---|
| 768 | self.assertEqual(math.pow(0.9, INF), 0.)
|
|---|
| 769 | self.assertEqual(math.pow(0.1, INF), 0.)
|
|---|
| 770 | self.assertEqual(math.pow(-0.1, INF), 0.)
|
|---|
| 771 | self.assertEqual(math.pow(-0.9, INF), 0.)
|
|---|
| 772 | self.assertEqual(math.pow(-1.1, INF), INF)
|
|---|
| 773 | self.assertEqual(math.pow(-1.9, INF), INF)
|
|---|
| 774 |
|
|---|
| 775 | # pow(x, y) should work for x negative, y an integer
|
|---|
| 776 | self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
|
|---|
| 777 | self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
|
|---|
| 778 | self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
|
|---|
| 779 | self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
|
|---|
| 780 | self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
|
|---|
| 781 | self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
|
|---|
| 782 | self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
|
|---|
| 783 | self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
|
|---|
| 784 | self.assertRaises(ValueError, math.pow, -2.0, -0.5)
|
|---|
| 785 | self.assertRaises(ValueError, math.pow, -2.0, 0.5)
|
|---|
| 786 |
|
|---|
| 787 | # the following tests have been commented out since they don't
|
|---|
| 788 | # really belong here: the implementation of ** for floats is
|
|---|
| 789 | # independent of the implementation of math.pow
|
|---|
| 790 | #self.assertEqual(1**NAN, 1)
|
|---|
| 791 | #self.assertEqual(1**INF, 1)
|
|---|
| 792 | #self.assertEqual(1**NINF, 1)
|
|---|
| 793 | #self.assertEqual(1**0, 1)
|
|---|
| 794 | #self.assertEqual(1.**NAN, 1)
|
|---|
| 795 | #self.assertEqual(1.**INF, 1)
|
|---|
| 796 | #self.assertEqual(1.**NINF, 1)
|
|---|
| 797 | #self.assertEqual(1.**0, 1)
|
|---|
| 798 |
|
|---|
| 799 | def testRadians(self):
|
|---|
| 800 | self.assertRaises(TypeError, math.radians)
|
|---|
| 801 | self.ftest('radians(180)', math.radians(180), math.pi)
|
|---|
| 802 | self.ftest('radians(90)', math.radians(90), math.pi/2)
|
|---|
| 803 | self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
|
|---|
| 804 |
|
|---|
| 805 | def testSin(self):
|
|---|
| 806 | self.assertRaises(TypeError, math.sin)
|
|---|
| 807 | self.ftest('sin(0)', math.sin(0), 0)
|
|---|
| 808 | self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
|
|---|
| 809 | self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
|
|---|
| 810 | try:
|
|---|
| 811 | self.assertTrue(math.isnan(math.sin(INF)))
|
|---|
| 812 | self.assertTrue(math.isnan(math.sin(NINF)))
|
|---|
| 813 | except ValueError:
|
|---|
| 814 | self.assertRaises(ValueError, math.sin, INF)
|
|---|
| 815 | self.assertRaises(ValueError, math.sin, NINF)
|
|---|
| 816 | self.assertTrue(math.isnan(math.sin(NAN)))
|
|---|
| 817 |
|
|---|
| 818 | def testSinh(self):
|
|---|
| 819 | self.assertRaises(TypeError, math.sinh)
|
|---|
| 820 | self.ftest('sinh(0)', math.sinh(0), 0)
|
|---|
| 821 | self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
|
|---|
| 822 | self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
|
|---|
| 823 | self.assertEqual(math.sinh(INF), INF)
|
|---|
| 824 | self.assertEqual(math.sinh(NINF), NINF)
|
|---|
| 825 | self.assertTrue(math.isnan(math.sinh(NAN)))
|
|---|
| 826 |
|
|---|
| 827 | def testSqrt(self):
|
|---|
| 828 | self.assertRaises(TypeError, math.sqrt)
|
|---|
| 829 | self.ftest('sqrt(0)', math.sqrt(0), 0)
|
|---|
| 830 | self.ftest('sqrt(1)', math.sqrt(1), 1)
|
|---|
| 831 | self.ftest('sqrt(4)', math.sqrt(4), 2)
|
|---|
| 832 | self.assertEqual(math.sqrt(INF), INF)
|
|---|
| 833 | self.assertRaises(ValueError, math.sqrt, NINF)
|
|---|
| 834 | self.assertTrue(math.isnan(math.sqrt(NAN)))
|
|---|
| 835 |
|
|---|
| 836 | def testTan(self):
|
|---|
| 837 | self.assertRaises(TypeError, math.tan)
|
|---|
| 838 | self.ftest('tan(0)', math.tan(0), 0)
|
|---|
| 839 | self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
|
|---|
| 840 | self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
|
|---|
| 841 | try:
|
|---|
| 842 | self.assertTrue(math.isnan(math.tan(INF)))
|
|---|
| 843 | self.assertTrue(math.isnan(math.tan(NINF)))
|
|---|
| 844 | except:
|
|---|
| 845 | self.assertRaises(ValueError, math.tan, INF)
|
|---|
| 846 | self.assertRaises(ValueError, math.tan, NINF)
|
|---|
| 847 | self.assertTrue(math.isnan(math.tan(NAN)))
|
|---|
| 848 |
|
|---|
| 849 | def testTanh(self):
|
|---|
| 850 | self.assertRaises(TypeError, math.tanh)
|
|---|
| 851 | self.ftest('tanh(0)', math.tanh(0), 0)
|
|---|
| 852 | self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
|
|---|
| 853 | self.ftest('tanh(inf)', math.tanh(INF), 1)
|
|---|
| 854 | self.ftest('tanh(-inf)', math.tanh(NINF), -1)
|
|---|
| 855 | self.assertTrue(math.isnan(math.tanh(NAN)))
|
|---|
| 856 | # check that tanh(-0.) == -0. on IEEE 754 systems
|
|---|
| 857 | if float.__getformat__("double").startswith("IEEE"):
|
|---|
| 858 | self.assertEqual(math.tanh(-0.), -0.)
|
|---|
| 859 | self.assertEqual(math.copysign(1., math.tanh(-0.)),
|
|---|
| 860 | math.copysign(1., -0.))
|
|---|
| 861 |
|
|---|
| 862 | def test_trunc(self):
|
|---|
| 863 | self.assertEqual(math.trunc(1), 1)
|
|---|
| 864 | self.assertEqual(math.trunc(-1), -1)
|
|---|
| 865 | self.assertEqual(type(math.trunc(1)), int)
|
|---|
| 866 | self.assertEqual(type(math.trunc(1.5)), int)
|
|---|
| 867 | self.assertEqual(math.trunc(1.5), 1)
|
|---|
| 868 | self.assertEqual(math.trunc(-1.5), -1)
|
|---|
| 869 | self.assertEqual(math.trunc(1.999999), 1)
|
|---|
| 870 | self.assertEqual(math.trunc(-1.999999), -1)
|
|---|
| 871 | self.assertEqual(math.trunc(-0.999999), -0)
|
|---|
| 872 | self.assertEqual(math.trunc(-100.999), -100)
|
|---|
| 873 |
|
|---|
| 874 | class TestTrunc(object):
|
|---|
| 875 | def __trunc__(self):
|
|---|
| 876 | return 23
|
|---|
| 877 |
|
|---|
| 878 | class TestNoTrunc(object):
|
|---|
| 879 | pass
|
|---|
| 880 |
|
|---|
| 881 | self.assertEqual(math.trunc(TestTrunc()), 23)
|
|---|
| 882 |
|
|---|
| 883 | self.assertRaises(TypeError, math.trunc)
|
|---|
| 884 | self.assertRaises(TypeError, math.trunc, 1, 2)
|
|---|
| 885 | self.assertRaises((AttributeError, TypeError), math.trunc,
|
|---|
| 886 | TestNoTrunc())
|
|---|
| 887 |
|
|---|
| 888 | def testIsnan(self):
|
|---|
| 889 | self.assertTrue(math.isnan(float("nan")))
|
|---|
| 890 | self.assertTrue(math.isnan(float("inf")* 0.))
|
|---|
| 891 | self.assertFalse(math.isnan(float("inf")))
|
|---|
| 892 | self.assertFalse(math.isnan(0.))
|
|---|
| 893 | self.assertFalse(math.isnan(1.))
|
|---|
| 894 |
|
|---|
| 895 | def testIsinf(self):
|
|---|
| 896 | self.assertTrue(math.isinf(float("inf")))
|
|---|
| 897 | self.assertTrue(math.isinf(float("-inf")))
|
|---|
| 898 | self.assertTrue(math.isinf(1E400))
|
|---|
| 899 | self.assertTrue(math.isinf(-1E400))
|
|---|
| 900 | self.assertFalse(math.isinf(float("nan")))
|
|---|
| 901 | self.assertFalse(math.isinf(0.))
|
|---|
| 902 | self.assertFalse(math.isinf(1.))
|
|---|
| 903 |
|
|---|
| 904 | # RED_FLAG 16-Oct-2000 Tim
|
|---|
| 905 | # While 2.0 is more consistent about exceptions than previous releases, it
|
|---|
| 906 | # still fails this part of the test on some platforms. For now, we only
|
|---|
| 907 | # *run* test_exceptions() in verbose mode, so that this isn't normally
|
|---|
| 908 | # tested.
|
|---|
| 909 |
|
|---|
| 910 | if verbose:
|
|---|
| 911 | def test_exceptions(self):
|
|---|
| 912 | try:
|
|---|
| 913 | x = math.exp(-1000000000)
|
|---|
| 914 | except:
|
|---|
| 915 | # mathmodule.c is failing to weed out underflows from libm, or
|
|---|
| 916 | # we've got an fp format with huge dynamic range
|
|---|
| 917 | self.fail("underflowing exp() should not have raised "
|
|---|
| 918 | "an exception")
|
|---|
| 919 | if x != 0:
|
|---|
| 920 | self.fail("underflowing exp() should have returned 0")
|
|---|
| 921 |
|
|---|
| 922 | # If this fails, probably using a strict IEEE-754 conforming libm, and x
|
|---|
| 923 | # is +Inf afterwards. But Python wants overflows detected by default.
|
|---|
| 924 | try:
|
|---|
| 925 | x = math.exp(1000000000)
|
|---|
| 926 | except OverflowError:
|
|---|
| 927 | pass
|
|---|
| 928 | else:
|
|---|
| 929 | self.fail("overflowing exp() didn't trigger OverflowError")
|
|---|
| 930 |
|
|---|
| 931 | # If this fails, it could be a puzzle. One odd possibility is that
|
|---|
| 932 | # mathmodule.c's macros are getting confused while comparing
|
|---|
| 933 | # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE
|
|---|
| 934 | # as a result (and so raising OverflowError instead).
|
|---|
| 935 | try:
|
|---|
| 936 | x = math.sqrt(-1.0)
|
|---|
| 937 | except ValueError:
|
|---|
| 938 | pass
|
|---|
| 939 | else:
|
|---|
| 940 | self.fail("sqrt(-1) didn't raise ValueError")
|
|---|
| 941 |
|
|---|
| 942 | @requires_IEEE_754
|
|---|
| 943 | def test_testfile(self):
|
|---|
| 944 | for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
|
|---|
| 945 | # Skip if either the input or result is complex, or if
|
|---|
| 946 | # flags is nonempty
|
|---|
| 947 | if ai != 0. or ei != 0. or flags:
|
|---|
| 948 | continue
|
|---|
| 949 | if fn in ['rect', 'polar']:
|
|---|
| 950 | # no real versions of rect, polar
|
|---|
| 951 | continue
|
|---|
| 952 | func = getattr(math, fn)
|
|---|
| 953 | try:
|
|---|
| 954 | result = func(ar)
|
|---|
| 955 | except ValueError:
|
|---|
| 956 | message = ("Unexpected ValueError in " +
|
|---|
| 957 | "test %s:%s(%r)\n" % (id, fn, ar))
|
|---|
| 958 | self.fail(message)
|
|---|
| 959 | except OverflowError:
|
|---|
| 960 | message = ("Unexpected OverflowError in " +
|
|---|
| 961 | "test %s:%s(%r)\n" % (id, fn, ar))
|
|---|
| 962 | self.fail(message)
|
|---|
| 963 | self.ftest("%s:%s(%r)" % (id, fn, ar), result, er)
|
|---|
| 964 |
|
|---|
| 965 | @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
|
|---|
| 966 | "test requires IEEE 754 doubles")
|
|---|
| 967 | def test_mtestfile(self):
|
|---|
| 968 | ALLOWED_ERROR = 20 # permitted error, in ulps
|
|---|
| 969 | fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}"
|
|---|
| 970 |
|
|---|
| 971 | failures = []
|
|---|
| 972 | for id, fn, arg, expected, flags in parse_mtestfile(math_testcases):
|
|---|
| 973 | func = getattr(math, fn)
|
|---|
| 974 |
|
|---|
| 975 | if 'invalid' in flags or 'divide-by-zero' in flags:
|
|---|
| 976 | expected = 'ValueError'
|
|---|
| 977 | elif 'overflow' in flags:
|
|---|
| 978 | expected = 'OverflowError'
|
|---|
| 979 |
|
|---|
| 980 | try:
|
|---|
| 981 | got = func(arg)
|
|---|
| 982 | except ValueError:
|
|---|
| 983 | got = 'ValueError'
|
|---|
| 984 | except OverflowError:
|
|---|
| 985 | got = 'OverflowError'
|
|---|
| 986 |
|
|---|
| 987 | accuracy_failure = None
|
|---|
| 988 | if isinstance(got, float) and isinstance(expected, float):
|
|---|
| 989 | if math.isnan(expected) and math.isnan(got):
|
|---|
| 990 | continue
|
|---|
| 991 | if not math.isnan(expected) and not math.isnan(got):
|
|---|
| 992 | if fn == 'lgamma':
|
|---|
| 993 | # we use a weaker accuracy test for lgamma;
|
|---|
| 994 | # lgamma only achieves an absolute error of
|
|---|
| 995 | # a few multiples of the machine accuracy, in
|
|---|
| 996 | # general.
|
|---|
| 997 | accuracy_failure = acc_check(expected, got,
|
|---|
| 998 | rel_err = 5e-15,
|
|---|
| 999 | abs_err = 5e-15)
|
|---|
| 1000 | elif fn == 'erfc':
|
|---|
| 1001 | # erfc has less-than-ideal accuracy for large
|
|---|
| 1002 | # arguments (x ~ 25 or so), mainly due to the
|
|---|
| 1003 | # error involved in computing exp(-x*x).
|
|---|
| 1004 | #
|
|---|
| 1005 | # XXX Would be better to weaken this test only
|
|---|
| 1006 | # for large x, instead of for all x.
|
|---|
| 1007 | accuracy_failure = ulps_check(expected, got, 2000)
|
|---|
| 1008 |
|
|---|
| 1009 | else:
|
|---|
| 1010 | accuracy_failure = ulps_check(expected, got, 20)
|
|---|
| 1011 | if accuracy_failure is None:
|
|---|
| 1012 | continue
|
|---|
| 1013 |
|
|---|
| 1014 | if isinstance(got, str) and isinstance(expected, str):
|
|---|
| 1015 | if got == expected:
|
|---|
| 1016 | continue
|
|---|
| 1017 |
|
|---|
| 1018 | fail_msg = fail_fmt.format(id, fn, arg, expected, got)
|
|---|
| 1019 | if accuracy_failure is not None:
|
|---|
| 1020 | fail_msg += ' ({})'.format(accuracy_failure)
|
|---|
| 1021 | failures.append(fail_msg)
|
|---|
| 1022 |
|
|---|
| 1023 | if failures:
|
|---|
| 1024 | self.fail('Failures in test_mtestfile:\n ' +
|
|---|
| 1025 | '\n '.join(failures))
|
|---|
| 1026 |
|
|---|
| 1027 |
|
|---|
| 1028 | def test_main():
|
|---|
| 1029 | from doctest import DocFileSuite
|
|---|
| 1030 | suite = unittest.TestSuite()
|
|---|
| 1031 | suite.addTest(unittest.makeSuite(MathTests))
|
|---|
| 1032 | suite.addTest(DocFileSuite("ieee754.txt"))
|
|---|
| 1033 | run_unittest(suite)
|
|---|
| 1034 |
|
|---|
| 1035 | if __name__ == '__main__':
|
|---|
| 1036 | test_main()
|
|---|
